Each of Exercises 25–36 gives a formula for a function y=f(x). In each case, find f^(-1)(x) and identify the domain and range of f^(-1). As a check, show that f(f^(-1)(x))=f^(-1)(f(x))=x.
f(x) = (x + b) / (x − 2), b > −2 and constant
Evaluate the integrals in Exercises 39–56.
52. ∫(from π/4 to π/2)cot(t)dt
In Exercises 139–142, find the length of each curve.
139. y = (1/2)(e^x + e^(−x)) from x = 0 to x = 1.
143.
b. Find the average value of ln(x) over [1, e].
Use l’Hôpital’s rule to find the limits in Exercises 7–52.
49. lim (x → 0) (x - sin x) / (x tan x)
Use l’Hôpital’s rule to find the limits in Exercises 7–52.
12. lim (x → ∞) (x - 8x²) / (12x² + 5x)
